Question

Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:

Weight (gm)	50-60	60-70	70-80	80-90	90-100	100-110	110-120	120-130
Frequency	8	10	12	16	18	14	12	10

(i) Calculate the cumulative frequencies.

(ii) Draw the cumulative frequency curve and from it determines the median weight of the potatoes.

Answer 1

(i)We write the given data in the cumulative frequency table.

Marks	frequency f	Cumulative frequency c.f
50-60	8	8
60-70	10	18
70-80	12	30
80-90	16	46
90-100	18	64
100-110	14	78
110-120	12	90
120-130	10	100

(ii)To represent the data in the table graphically, we mark the upper limits of the class intervals on

the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis ( y-axis),

Plot the points $(60,8),(70,18),(80,30),(90,46),(100,64),(110,78),(120,90)$ and $(130,100)$ on the graph.

Join the points with the freehand. We get an ogive as shown:

Here $n=100$ which is even.

So $median=\left(n/2^{th}term\right)$

$=\left(100/2^{th}term\right)$

$=\left({50}^{th}term\right)$

Now mark a point A ($50$) on the Y-axis and from A draw a line parallel to X-axis meeting the curve at P. From P, draw a perpendicular on x-axis meeting it at Q.

Q is the median.

$Q=93gm.$

Hence the median is $93$.